3. Fluid force Ff (lift and drag) acting on the surface of the grain. The fluid force varies with
the velocity field and with the properties of the fluid.
The relative magnitude of these forces determines whether the grain moves or not.
For the individual grain, the body force is:
Fg = gρ s K 2 D3
(3.23)
s
where:
=
Density of the grain
ρs
=
Volumetric coefficient
K2
Ds
=
Grain diameter
=
Volume of the grain
K 2D3
s
For convenience, the fluid forces acting on the grain are divided into three components:
(1)
The form drag component FD
FD = CDK 1D 2ρ (V 2 / 2)
(3.24)
s
(2)
The viscous drag component FV
FV = C SK 1D 2 τ
(3.25)
s
(3)
The buoyant force component FB
FB = gρK 2 D3
(3.26)
s
where:
CD
=
Drag coefficient
=
Coefficient associated with the area of the grain subjected to form drag and
K1
shear (the term K 1D 2 represents the cross-sectional area of the grain)
s
K2
=
Volumetric coefficient of the grain
Ds
=
Diameter of the grain
v
=
Velocity in the vicinity of the grain
=
Coefficient of shear
Cs
=
Average viscous shear stress
τ
The external forces Fn depend on the values of the fluid and body forces FB. Under
conditions of no flow, the fluid force is Ff = FB. There is no form or viscous drag. Then the
external force Fn is Fn = Fg FB or
Fn = (ρ s - ρ) gK 2 D3
(3.27)
s
3.34
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